论文标题
库奇和布尔扎诺之间的连续性：先例和优先事项的问题
Continuity between Cauchy and Bolzano: Issues of antecedents and priority
论文作者
论文摘要
在1970年发表的一篇论文中，格拉顿·吉尼斯（Grattan-Guinness）认为，凯奇（Cauchy）在他的1821年书Cours d'Analyze中可能使Bolzano的书Rein Analytischer Beweis（RB）窃了，该书于1817年首次发表。该论文随后在几项工作中被剥夺了一些假设，但仍被认为是假设的。特别是，通常认为凯奇没有在Bolzano在RB中发展其功能的连续性的概念，并且这两个概念本质上都是相同的。我们认为，这两个假设都是不正确的，并且令人难以置信的是，凯奇对这种概念的最初洞察力最终进化为使用无穷小的方法，可能是从布尔扎诺的作品中借来的。此外，我们考虑了Bolzano对这一概念的兴趣，并专注于他对Kästner的定义的讨论（在他1766年的第183条中），前者似乎至少部分歪曲了这一定义。 考奇（Cauchy）对连续性的处理至少可以追溯到他的1817年课程摘要，这是Grattan-Guinness的pla窃假设的关键组成部分（Cauchy在1818年在巴黎图书馆阅读了RB后可能会取消RB的连续性）。我们在Kästner和早期作者的著作中探讨了凯奇和布尔扎诺连续性的先例。
In a paper published in 1970, Grattan-Guinness argued that Cauchy, in his 1821 book Cours d'Analyse, may have plagiarized Bolzano's book Rein analytischer Beweis (RB), first published in 1817. That paper was subsequently discredited in several works, but some of its assumptions still prevail today. In particular, it is usually considered that Cauchy did not develop his notion of the continuity of a function before Bolzano developed his in RB, and that both notions are essentially the same. We argue that both assumptions are incorrect, and that it is implausible that Cauchy's initial insight into that notion, which eventually evolved to an approach using infinitesimals, could have been borrowed from Bolzano's work. Furthermore, we account for Bolzano's interest in that notion and focus on his discussion of a definition by Kästner (in Section 183 of his 1766 book), which the former seems to have misrepresented at least partially. Cauchy's treatment of continuity goes back at least to his 1817 course summaries, refuting a key component of Grattan-Guinness' plagiarism hypothesis (that Cauchy may have lifted continuity from RB after reading it in a Paris library in 1818). We explore antecedents of Cauchy and Bolzano continuity in the writings of Kästner and earlier authors.
